After completing
his doctoral work in August, 2004, Dr. Xiong Zhang put together
a three-dimensional transient simulation of the deformations and
stresses and strains in an L-Shaped residence with walls, windows,
and doors under the influence of a tree and its root zone responding
to the weather patterns in Arlington, Texas. This work was the first
of its kind in modeling movement of a residential foundation.

Dr. Zhang developed
five models to run the analysis which Dr. Lytton presented to an
audience of 70.

The simulation
was run on Texas A&M's super computer and covered two years
of the entire building responding to the movements of the foundation
soil as a result of the climate. The software used as ABAQUS, a
3D Finite Element Analysis program that allows water to move through
the soil elements and element stiffness that can vary throughout
the analysis. Contact (jointed) elements were used to simulate the
soil-structure interaction. The foundation and superstructure were
modelled using general shell elements.

The software
was set up to solve rather complex partial differential equations
at each joint for each time step. The time step used was a 24-hour
day so that 730 time steps were analyzed, using approximately 24
hours of super computer run time for each problem. Two problems
were analyzed, with the difference being the tree location relative
to the foundation.

The slab was
taken from one of the example problems (Appendix A.4) in the soon-to-be-published
Post-Tensioning Institute 3rd Edition Design Manual. The 4"
slab with 12"x34" deep grade beams was simplified as a
16" uniform slab that gave similar stiffness. The laboratory
tests for the Arlington TX site that were input into the analysis
included liguid limit, plastic limit, %-200 sieve and %-2 microns
hydrometer tests. The exterior walls were simulated as brick veneer
and the interior walls were simulated as stud walls with drywall
sheeting.

Dr. Zhang's
analysis was setup to simulate a residence and the soil conditions
that are typical of Houston and other parts of Texas. Four shallow
footings in Arlington had been monitored for movement for two years
and that data was plotted and used in the analysis. The weather
used was actual historical data from Arlington TX in the 99/01 period.
The method used to compute evapo-transpiration was the FAO-56 Penman-Monteith
method and accounted for solar radiation, relative humidity, wind
speed, rainfall, vegetation types, soil permeability, and soil water
content.

Dr. Zhang had
translated the simulation data into several movies that separately
showed the changing patterns of soil and slab movement, the suction
in the supporting soil, and the slab directional moment, shear,
stress, strain and liftoff patterns that occur over time. The movies
also showed where the stresses concentrate above the doors and windows
as well as in the foundation slab.

Some points
made by Dr. Lytton during his presentation:

Diffusion
decreases as suction increases.

Soil with
cracks has a diffusion rate of about 100 times that of non-cracked
soil.

When modeling
soil in FEA programs, use the long term soil modulus (on the order
of Es = 1000 psi), rather than what is obtained from short-term
tests (Es of about 15,000 psi).

Matric Suction
is the tensile pressure of water.

Water has
a tensile strength of 3000 - 3600 psi when confined, but this
goes to zero when the suction is low.

Mechanical
stress (weight of foundation and superstructure) has relatively
little effect on the other soil properties as compared to that
of suction.

When the
tree was modelled near the corner of the foundation, they found
the foundation cantilevered up to 4 meters (13 ft) in the vicinity
of the tree.

The data presented
was about 2 Gigabytes in size and too large to include on the FPA
website. However Dr. Zhang took a snapshot of each movie and included
the snapshots as slides in his presentation. To download the slide
show presentation, click
here

To read summaries
of prior FPA presentations by Dr. Lytton and Dr. Bulut:

Dr. Lytton
and Dr. Bulut presented to the FPA in August
2001 on the filter paper method and new software being developed
to make finite element analyses of foundations on expansive soils
using elastic half-space.

Dr. Lytton
and Dr. Aubeny presented to the FPA in August
2002 on using suction to determine shallow slope failures.

Dr. Robert
L. Lytton , P.E., Dr. Charles P. Aubeny, and Dr. Rifat Bulut in August 2003 on
how to run suction tests.